split big metric into small ones

hi everyone

i have a question

how to divide a (513*513) matrix into smaller 29241 (3*3) matrices ?

Answer 1

[Adam Danz]

"how to divide a (513*513) matrix into smaller 29241 (3*3) matrices ?"

"mc" below is a 171 x 171 cell array of your 29241 sub-matrices (each 3x3).

m = magic(513); % fake data 513x513 matrix
mc = mat2cell(m,repmat(3,1,size(m,1)/3), repmat(3,1,size(m,1)/3)); 

"i want to multiply each submatrix by a matrix of [1 2 4;128 0 8;64 32 16] these weights"

"mcw" below is the same cell array multiplied by your weight matrix.

weight = [1 2 4;128 0 8;64 32 16] ; 
mcw = cellfun(@(x)x.*weight, mc, 'UniformOutput', false); 

Answer 2

[Star Strider]

You create a 3D matrix, that is (9,9,3249):

M = rand(513);
R = reshape(M, 9, 9, []);
Rsize = size(R)

Rsize =
           9           9        3249

[Ahmed Saad]

i tried this method and this is the result but i want separate matrices to perform further calculation on each one

[Star Strider]

You would have to address them individually.

For example, as ‘R(:,:,1)’, ‘R(:,:,2)’ ... and so for the others.

Depending on what operations you want to do, you might be able to vectorise them. Otherwise, you would need a for loop.

I cannot suggest a method without knowing the calculations you want to do.

[Ahmed Saad]

i want to multiply each submatrix by a matrix of [1 2 4;128 0 8;64 32 16] these weights

[Star Strider]

That is not possible. You are multiplying (9x9) matrices by a (3x3) matrix.

[Ahmed Saad]

no i shifted from 9*9 matcries to 3*3, i changed the original question

[Star Strider]

It would have been straightforward for you to change my code — in my Answer that you originally Accepted — to produce your (3x3) matrices, quite simply:

R = reshape(M, 3, 3, []);  

This is trivial.

I then would have used loops to do the multiplications, depending on what you want to do, since there are two ways to do the matrix multiplication: element-wise array multiplication and matrix multiplication, since you did not mention which one you wanted to do:

for k = 1:size(R,3)
    Out33(:,:,k) = R(:,:,k).*W;                    % Out Is (3x3x29241) — Array Multiplication
end

or:

for k = 1:size(R,3)
    Out1(:,:,k) = R(:,:,k)*W;                      % Out Is (3x3x29241) — Matrix Multiplication
end

My code is also more efficient.

The reshape call and each loop require:

Elapsed time is 0.000089 seconds.
Elapsed time is 0.066342 seconds.
Elapsed time is 0.064366 seconds.

respectively.

The mat2cell call and cellfun call require:

Elapsed time is 0.052617 seconds.
Elapsed time is 0.114920 seconds.

respectively.

[Adam Danz]

"I then would have used loops to do the multiplications"

Actually, you wouldn't need a for-loop.

m = magic(513);  %fake data
weight = [1 2 4;128 0 8;64 32 16] ; 
ma = reshape(m, 3, 3, []);
out = ma .* weight; % assuming element-wise multiplication

This is faster, indeed.

[Star Strider]

I decided to use loops in the event that the Question changed yet again, to add another requirement or calculation, or to change the matrix size. Again.

Moving target ...

[Adam Danz]

I must have first seen the question after it's final form.

+1 for getting the OP there.

[Ahmed Saad]

thanks guys for your answers it helped alot

actually i have a 30 different (513*513) matrcies that i need to do the same for each one then add the element in each matrix cell to generate one number from each matrix so i end up with one number for each of the 30 matrcies and then gather them all together in one column and for the multiplication is is an element wise multiplication.

[Star Strider]

I am still not certain what you want to do.

If you want to apply the weighting matrix to each sub-matrix and then sum the weighted sub-matrices, it would be more efficient to do the summation first, then multiply by the weighting matrix:

R = reshape(M, 3, 3, []);
RWsum = sum(R,3).*W;

The result is the same.

I do not know how you want to get one number for each (513x513) matrix. If you define it as the sum of the elements of the (3x3) weighted sum of the matrices, convert it to a column vector, then sum the column vector:

MatrixNumber = sum(RWsum(:));

You could then put these into a very efficient for loop to get results for each of your 30 matrices.